Trial and improvement, or simultaneous equation?
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Trial and improvement, or simultaneous equation?
As you may realise from my question my maths is not great, there are some question types on past 11plus papers that im beginning to look at with my DS and i am wondering
x+y=39
x-y=7
what is x?
I just do trial and improvement for this style of question, its all I know, but my older children are telling me this is a simultaneous equation and I need to teach My DS son this, which I'll have to learn myself, are they correct?
Similar questions are : if P is 70 bigger than Q and P+Q =110, what is the value of Q?.. Again I used the trial and improvement method?
All advice appreciated, Thank-you.
x+y=39
x-y=7
what is x?
I just do trial and improvement for this style of question, its all I know, but my older children are telling me this is a simultaneous equation and I need to teach My DS son this, which I'll have to learn myself, are they correct?
Similar questions are : if P is 70 bigger than Q and P+Q =110, what is the value of Q?.. Again I used the trial and improvement method?
All advice appreciated, Thank-you.
Re: Trial and improvement, or simultaneous equation?
make either y the subject of the equation..
x+y=39, therefore..y=39-x (take x to the other side of the equation, it then goes from being +ve to -ve
x-y=7
therefore, replace the y in the second equation with the re-jigged equation from the first..
x-(39-x)=7
x-39+x=7 (opening up the brackets)
2x-39=7
2x=7+39 (39 becomes +ve going to the otherside of the = sign)
2x=46
therefore x=23
cool, that was from 1987!
Hope that is clear as mud...someone else can put it down better I feel!
x+y=39, therefore..y=39-x (take x to the other side of the equation, it then goes from being +ve to -ve
x-y=7
therefore, replace the y in the second equation with the re-jigged equation from the first..
x-(39-x)=7
x-39+x=7 (opening up the brackets)
2x-39=7
2x=7+39 (39 becomes +ve going to the otherside of the = sign)
2x=46
therefore x=23
cool, that was from 1987!
Hope that is clear as mud...someone else can put it down better I feel!
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Re: Trial and improvement, or simultaneous equation?
That works, but it's messy.
x+y=39
x-y=7
Just add the two equations together. The ys cancel out.
(x + x) + (y - y) = (39 + 7)
2x = 46
x = 23
To check your workings, get y out of the first equation (39 - x = 16) and check the second equation is still true (23 - 16 = 7).
Alternatively, for this special case (and to be honest, I'd be surprised if general simultaneous equations are required at 11+, so this special case may be all that's needed), 7 and 39 are separated by 2y (think of it on a number line). So x must be half way between them 7 + 1/2 (39-7).
x+y=39
x-y=7
Just add the two equations together. The ys cancel out.
(x + x) + (y - y) = (39 + 7)
2x = 46
x = 23
To check your workings, get y out of the first equation (39 - x = 16) and check the second equation is still true (23 - 16 = 7).
Alternatively, for this special case (and to be honest, I'd be surprised if general simultaneous equations are required at 11+, so this special case may be all that's needed), 7 and 39 are separated by 2y (think of it on a number line). So x must be half way between them 7 + 1/2 (39-7).
Last edited by tokyonambu on Sun Jul 03, 2011 8:28 pm, edited 1 time in total.
Re: Trial and improvement, or simultaneous equation?
That's works too.
I have taught my method for many years and has always come up in 11+ exams.
Your method is for a slightly older child, not 11+ in my opinion.
I have taught my method for many years and has always come up in 11+ exams.
Your method is for a slightly older child, not 11+ in my opinion.
Re: Trial and improvement, or simultaneous equation?
Just some advice, always better to explain the steps involved. For example, explain why the two equations should be added together.
Re: Trial and improvement, or simultaneous equation?
I would resolve it this way:Precious wrote: Similar questions are : if P is 70 bigger than Q and P+Q =110, what is the value of Q?.. Again I used the trial and improvement method?
The exercise give these two information:
P = Q + 70
P+ Q = 110
I use the fist equation into the second which becomes:
Q + 70 + Q = 110
so 2Q = 110-70
so 2Q = 40
so Q = 20
therefore P= 110 -20 = 90
good luck
Re: Trial and improvement, or simultaneous equation?
The most simple way to explain it to 'pre-algebra' students is:
Take the difference between the two numbers away from the total of the two numbers:
39 - 7 = 32
Then halve this answer:
32 / 2 = 16
This will give the smaller of the two numbers: 16
The larger number is just found by adding 16 and 7: 23
x = 23, y = 16
No algebra involved!
Take the difference between the two numbers away from the total of the two numbers:
39 - 7 = 32
Then halve this answer:
32 / 2 = 16
This will give the smaller of the two numbers: 16
The larger number is just found by adding 16 and 7: 23
x = 23, y = 16
No algebra involved!
Re: Trial and improvement, or simultaneous equation?
That's not to say algebra is not needed for some of the entrance exams